The only case where it could be an issue is at bootup, when the subsystem simply does not have enough entropy. OpenBSD solved that by storing a seed for next bootup at the end of boot and during shutdown.
> RSA and DSA can fail catastrophically when used with malfunctioning random number generators ... network survey of TLS and SSH servers and present evidence that vulnerable keys are surprisingly widespread ... we are able to obtain RSA private keys for 0.50% of TLS hosts and 0.03% of SSH hosts, because their public keys shared nontrivial common factors due to entropy problems, and DSA private keys for 1.03% of SSH hosts, because of insufficient signature randomness ... the vast majority appear to be headless or embedded devices ...
It is used as one source among many to seed the PRNG, so I think the answer is no.